Giant Orbital Anisotropy with Strong Spin–Orbit Coupling Established at the Pseudomorphic Interface of the Co/Pd Superlattice

Abstract Orbital anisotropy at interfaces in magnetic heterostructures has been key to pioneering spin–orbit‐related phenomena. However, modulating the interface's electronic structure to make it abnormally asymmetric has been challenging because of lack of appropriate methods. Here, the authors report that low‐energy proton irradiation achieves a strong level of inversion asymmetry and unusual strain at interfaces in [Co/Pd] superlattices through nondestructive, selective removal of oxygen from Co3O4/Pd superlattices during irradiation. Structural investigations corroborate that progressive reduction of Co3O4 into Co establishes pseudomorphic growth with sharp interfaces and atypically large tensile stress. The normal component of orbital to spin magnetic moment at the interface is the largest among those observed in layered Co systems, which is associated with giant orbital anisotropy theoretically confirmed, and resulting very large interfacial magnetic anisotropy is observed. All results attribute not only to giant orbital anisotropy but to enhanced interfacial spin–orbit coupling owing to the pseudomorphic nature at the interface. They are strongly supported by the observation of reversal of polarity of temperature‐dependent Anomalous Hall signal, a signature of Berry phase. This work suggests that establishing both giant orbital anisotropy and strong spin–orbit coupling at the interface is key to exploring spintronic devices with new functionalities.


Sum rule to calculate the ratio of orbital to spin magnetic moment
The x-ray magnetic circular dichroism (XMCD) was measured with 95% circularly polarized incident light in the normal direction of the superlattice plane at the 2A beamline of the Pohang Light Source. The total electron yield mode was used to obtain spectra at 300 K. An XAS measurement was performed at the Co L-edge to extract the XMCD spectra. XAS spectra from 2p → 3d dipole transitions represent the dependence on the parallel (μ + ) and anti-parallel alignments (μ -) of the magnetization directions with the photon helicity, as shown in Figure.
where p and q are negative in this case, which means that the directions of the orbital and spin magnetic moments in the superlattices are parallel. The m o /m s ratio is an important parameter when investigating how the orbital moment contributes to spin-orbit interaction in the superlattices. [1,2] Figure S1. XAS and XMCD spectra of the [M-Co/Pd] with a 4-Å-thick Co layer measured at the Co L 2,3 edges. The red and blue lines are XAS spectra measured when magnetizations of the superlattice were anti-parallel and parallel, respectively, to the incident direction of the 95% circular polarized xray. The solid yellow line is the integrated XMCD spectrum. p and q are explained in the article.

Estimation of the in-plane d-spacings of Co in the superlattices
A noticeable feature in the grazing incident x-ray diffraction (GIXRD) spectra of the [M-Co/Pd] and the [R-Co/Pd], as shown in Figures S2 (a) and (b), is that the shoulders of the primary peak, which are diffracted from Co (220) planes, start to be observed at t Co =~6Å and increase in their intensity with the t Co for both [M-Co/Pd] and [R-Co/Pd], which has also been reported in the literature. [3,4] Figure S2 (c) shows a schematic of the measurement setup. The primary peaks correspond to the (220) planes of the superlattice films whose normal vector is parallel to the in-plane direction. The primary peaks are resolved into three peaks (dotted lines in Figures. S2 (a) and (b)) based on the following two observations: 1) The intensity of the peak at the low angle in the primary peak increases relative to that at high angles when α is decreased from 0.33° to 0.22°. Because surface scattering can be enhanced at low incident angles, the peak at the low angle can mainly originate from the top of the film, that is, the Pd capping layer.
2) The intensity of the peak at the high angles does change considerably with the t Co , unlike the peak at the low angle, which implies that the peaks at the high angles can be assigned to the rest of the superlattice. Figures S2 (d) shows the anomalous x-ray scattering (AXS) spectra of the superlattices near the Co K-edge measured at the primary (220) Bragg peak in the GIXRD spectra. The variations of the integrated intensities as a function of the x-ray photon energy show intensity cusps near the Co K-edge for the selected thicknesses of the Co layer in the superlattices, which proves that the Co layers in the superlattices contribute to the primary (220) Bragg peak. The interatomic distances between Co atoms along the in-plane direction are estimated using the interplanar spacings (dspacings) of (220) for both strained and relaxed Co in terms of a compositional average d-spacing, as discussed below. Figure S3 shows the d-spacings obtained by the curve-fitting of the GIXRD spectra as a function of the t Co . On the other hand, an x-ray absorption spectroscopy (XAS) study confirms that the Co 3 O 4 superlattices are mostly reduced to the metallic phase. Therefore, all effects of the residual oxide phases in the [R-Co/Pd] are neglected in this study.
According to our observation, the strain state of both superlattices can be divided into three regimes in terms of the t Co , as indicated in Figure S3. The coherent regime (denoted as Regime I) is defined in the t Co range of 0-5 Å, where the strain was coherently sustained. When the t Co range is 6-9 Å, the intermediate regime (Regime II)   The following three assumptions are made to estimate d ave : 1) The Co layers are pseudomorphically grown on the Pd layers at the interfaces, while the Co lattices in the middle of Co layer have d Co(220) close to the bulk value due to the strain relaxation. 2) Because the gradual decrease in the d Co(220) with t Co was observed in the experiments, we assume that the superlattice system has a strain gradient [5] out of plane. And 3) The d ave can be estimated using Equation (3) in our case: Here = − , where and are the numbers of Co monolayers (MLs) with pseudomorphism and strain relaxation, respectively. The first term in the square bracket in Equation (S3) indicates the total thickness of Co before relaxation or the sum of the d-spacings with a gradual decrease in the d Co(220), whereas the second term represents the total thickness of Co after relaxation.
The estimated from the GIXRD results are shown in Figure S3 (bottom).

Method
First-principles density functional theory calculations were performed using the Vienna ab-initio simulation package [6] with the generalized gradient approximation [7] for the exchange-correlation potential. To reveal the origin of the enhanced PMA of the reduced Co 3 O 4 /Pd superlattice observed in the experiment, we investigated superlattices composed of 4-ML Pd and 5-ML Co, whose geometry is shown in Figure S4. To consider the 9.8% mismatch between the two-dimensional (2D) lattice constants of bulk Co (3.54 Å) and Pd (3.89 Å), we employed 2D lattice strains of 0% to 10%. Here, 0% strain implies the 2D lattice constant of Co (3.54 Å), and 9.8% strain corresponds to Pd (3.89 Å).   Figure S5 (d)).
As a result, ⟨m=±1,↑|L x |m=0,↓⟩ becomes stronger, which leads to the significantly enhanced PMA for the strained Co/Pd superlattice. Here, the up-spins (↑) and down-spins (↓) indicate the majority and minority spins, respectively. Similar behaviors are observed for the occupied majority m=±1 orbitals and the unoccupied minority m=0 orbitals of Co (S), which are denoted by arrows in Figure S5(d), as previously mentioned in the discussion on the MCA of the Co/Pd superlattice. However, a prominent peak of the minority m=±1 orbitals appears near the Fermi level of Co (S) under 9.8% strain (dotted arrow in Figure S5(d)), which negatively contributes to the MCA through ⟨m=±1,↑|L x |m=0,↓⟩ at the surface. This negative contribution is balanced by the positive contribution of ⟨m=±1,↑|L x |m=0,↓⟩.
9/13 Figure S5. Partial DOS of d orbitals of (a) the unstrained superlattice, (b) the superlattice with 9.8% strain, (c) the unstrained Co film, and (d) the Co film with 9.8% strain. I, S, and S-1 denote the interface, surface, and subsurface, respectively. The shaded region and the dashed and solid lines indicate m=±2, m=±1, and m=0, respectively. The Fermi level is set to zero in energy.
10/13 The analyzed orbital moments of Co in the un-strained and the strained Co/Pd and at the interface of Co/Pd are listed in Tables S1 and Table S2. The perpendicular components of total magnetic moment of Co in both Co/Pd are larger than the in-plane components, and the difference between the components is denoted m. The change in total orbital moments (m o ), which is a measure of orbital anisotropy, is 0.016 and 0.149 μ B for the un-strained and the strained Co/Pd, respectively. The m o /m s is also estimated for each case.

Analyses of Co magnetic moments in the un-strained and the strained Co/Pd
In Table S2, the orbital moments of Co only at the interface are listed. The m o are 0.008 and 0.032 μ B for the un-strained and the strained Co/Pd, respectively. We note here that the magnitudes of the magnetic moments in Table S2 are much smaller than those in Table S1 simply because the orbital moments of all Co in the superlattice are calculated and listed in Table S1. We confirmed that the magnetic moment of Co at the interface is the largest. Though the orbital moment from the subinterface contribution is not negligible, the orbital moment from the interface contribution is sufficiently large to demonstrate the main argument of this article.

Hydrogenation effect on MCA energy
To investigate the hydrogen effect on the MCA energy (E MCA ), we considered six different hydrogen sites, which were positioned at the tetrahedral and octahedral sites in the Co, Pd, and Co-Pd interface layers. Tetrahedral sites are energetically more stable than octahedral sites for all atomic layers. The hydrogen atom in the Co layer energetically favors over that in the Pd layer and the Co-Pd interface by 0.93 and 0.72 eV/f.u., respectively. As shown in Figure S6a, hydrogen contributes in-plane MCA regardless of its location, which is consistent with previous results. [8] The hydrogen atom in the Co layer significantly reduces the MCA energy. 12/13

Magnetic anisotropy estimation by areal method
The magnetic anisotropy energies (Ku) were estimated by the areal method [9]. At first, we measured the magnetic hysteresis loops for Co/Pd superlattices with a field-sweep along the in-plane (or the hard axis) and the film-normal (or the easy axis) directions using a vibrating sample magnetometer (VSM). Then, we estimated the magnetic anisotropy energies by calculating the difference in the area of the first quadrant of a hysteresis loop (H > 0; M > 0) between the two loops, the easy and the hard axis loops. The difference in the area for typical [R-Co/Pd] is shown as a shaded region in Fig. S7.